An electric power network includes buses connected to transmission lines. The buses are locally connected to generators and loads. Optimal power flow (OPF) analysis is often used for monitoring and controlling the operation of the network. The power flow depends, in part, on voltage magnitudes and phase angles. Power flows and voltage levels on the buses are optimized by minimizing an objective function subject to constraints, such as the magnitudes, phases, power transferred, generator capacity, thermal losses, and the like.
Most conventional OPF optimizations:                (i) Solve the problem in a centralized manner.        (ii) Do not exploit a topology of the network to distribute the optimization over the buses.        
Some conventional methods for distributing the optimization problem:                (i) Use the Schur complement method, also called iterative substructuring, to distribute the computation of a single step in the optimization problem.        (ii) When the optimization problem is distributed by dual decomposition, a conventional subgradient method is used for solving the optimization problem. The subgradient method converges sub-linearly to a solution.        
Thus, there remains a need to optimize power flows in electric power networks in an efficient and expedient manner by appropriately distributing the computations.
U.S. Pat. No. 6,625,520 describes a system and method for operating an electric power system that determines optimal power flow and available transfer capability of the electric power system based on the optimal power flow. The system derives data associated with an initial phase angle and maximum electric power value of a generator by determining mechanical output and electrical output of a generator, including a generator phase angle defined by a time function with a constraint condition that the generator phase angle does not exceed a preset value.